OME 1965 Problem 5

It is well-known that if $\frac{p}{q}=\frac{r}{s}$ , both of the expressions are also equal to $\frac{p-r}{q-s}$ . Now we write the equality $$\frac{3x-b}{3x-5b}=\frac{3a-4b}{3a-8b}.$$ The previous property shows that both fractions should be equal to $$\frac{3x-b-3a+4b}{3x-5b-3a+8b}=\frac{3x-3a+3b}{3x-3a+3b}=1.$$ However, the initial fractions given may not be equal to $1$ . Explain what is going on.